Accurate simulation of the present-day characteristics of mean and extreme precipitation remains a challenge for Earth system models, which is due in part to deficiencies in model physics (e.g., convective parameterization) and coarse resolution. High resolution (HR, ~25 km) configurations and replacing conventional convective parameterizations with cloud-resolving models (i.e., multiscale modeling framework, MMF) are the two promising directions that could help to improve the interaction between the subgrid-scale physical processes and the large-scale climate. Here, we evaluated and intercompare extreme precipitation statistics over the United States (US) as simulated in three configurations: low-resolution (LR), HR, and MMF, of the Energy Exascale Earth System Model (E3SMv1) by comparing their results with two gridded observations (CPC and IMERG). We first assess the models' abilities to simulate the frequency and amount of daily precipitation, followed by the spatial patterns of the wet and dry extreme indices, as defined by the Expert Team on Climate Change Detection and Indices (ETCCDI). Compared to the conventional model (i.e., E3SMv1-LR), both E3SMv1-MMF and E3SMv1-HR improve the tails of the frequency and amount distributions of daily precipitation over the entire US. E3SMv1-HR (E3SMv1-MMF) improves the winter (summer) spatial distribution of daily mean precipitation over the Southeast and western half of the US (Southeast US). Both the dry (i.e., consecutive dry days) and wet (i.e., consecutive wet days, maximum 5-day precipitation, and very wet days) extremes evaluated herein are better improved by both E3SMv1-MMF and E3SMv1-HR relative to E3SMv1-LR, although the summer dry bias is poorly represented in the E3SMv1-MMF despite improvements in wet extremes. Overall, E3SMv1-HR and E3SMv1-MMF improvements vary across seasons and subregions and are largely seen in subregions dominated by large-scale (e.g., extratropical cyclones) and smaller convective (i.e., mesoscale convective systems) precipitation systems.